Why, despite matching FPS, does the audio not match the video in the rendered file?
At the very beggining of the tutorial, he tells us that it may be problematic to work directly with the .mov file, depending on the FFMPEG version in use within your system.

So you should try to convert the movie source file into an images sequence, and import it in VSE. Then, import the audio of the the original .mov file, and sync it with the images sequence strip.